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If $${\text{co}}{{\text{s}}^4}\theta - {\sin ^4}\theta = \frac{2}{3},$$ then the value of $${\text{1}} - {\text{2}}{\sin ^2}\theta $$ is?
Answer & Solution
Correct Answer:
Option
C
$$\eqalign{
& {\text{co}}{{\text{s}}^4}\theta - {\sin ^4}\theta = \frac{2}{3} \cr
& \Rightarrow \left( {{\text{co}}{{\text{s}}^2}\theta - {{\sin }^2}\theta } \right)\left( {{\text{co}}{{\text{s}}^2}\theta + {{\sin }^2}\theta } \right) = \frac{2}{3} \cr
& \Rightarrow {\text{co}}{{\text{s}}^2}\theta - {\sin ^2}\theta = \frac{2}{3} \cr
& \Rightarrow 1 - {\sin ^2}\theta - {\sin ^2}\theta = \frac{2}{3} \cr
& \Rightarrow 1 - 2{\sin ^2}\theta = \frac{2}{3} \cr} $$
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